Spacecraft Drift Counteraction Optimal Control: Open-Loop and Receding Horizon Solutions

Continuous Optimization-Based Drift Counteraction Optimal Control: A Spacecraft Attitude Control Case Study

“…However, it is generally difficult to solve an HJB equation either analytically or numerically, especially considering that it may not admit a smooth solution. As a result, recent advances in DCOC have been in a discrete-time setting [7][8][9][10][11][12][13][14][15], which is more computationally tractable. Apart from computational benefits, a discrete-time formulation also leads to control solutions that are easily implementable with digital micro-controllers.…”

“…Apart from computational benefits, a discrete-time formulation also leads to control solutions that are easily implementable with digital micro-controllers. For discrete-time systems, DCOC approaches based on dynamic programming (DP) [7][8][9][10][11][12] and mixed-integer programming (MIP) [13][14][15] have been developed. However, both DP-based and MIP-based approaches are faced with computational challenges: The former can treat DCOC problems with general yield functional [7] but suffer from the curse of dimensionality [16];…”

“…discrete-time open-loop DCOC problem is proposed in [13][14][15]. However, because the number of integer variables in this MIP formulation is proportional to the planning horizon and the worst-case computational complexity of MIP grows combinatorially with the number of integer variables [17], computing numerical solutions to this MIP problem can be very challenging, especially for systems/problems that require longer planning horizons or shorter sampling periods.…”

“…For nonlinear systems, an MPC-based strategy based on linearized prediction models and the LP reformulation is investigated in [14,15]. However, these continuous relaxation-based approaches only provide approximate solutions to the original DCOC problem and do not guarantee maximum time-before-exit.…”

“…In this paper, we apply our continuous optimization approach to the original nonlinear spacecraft attitude dynamics model and demonstrate the effectiveness of our approach in maximizing the time-before-exit for the cases of two and three functioning RWs in numerical examples. In [14] and [15], a DCOC approach based on LP relaxation of an MIP formulation is implemented based on a linearized spacecraft attitude dynamics model. Our work here improves upon the previous work of [14] and [15] in the following two aspects: Firstly, when applied to a same model, our approach produces optimal solutions in terms of maximizing the time-before-exit, while the approach of [14] and [15] produces only approximate solutions to the original DCOC problem that may not achieve maximum time-before-exit.…”